It is the sovereign State (1 entity) casting its electoral vote, so splitting the vote makes less sense than a single winner. We're not a parliamentary style government.

If a state is one entity, it should have a single vote. Instead, there is a college of electors, and those electors should at least reflect the electoral outcome in the nominal congressional districts that they represent, as in Maine and Nebraska. (I know that's not how elector assignment generally works, but I think it's just as valid an interpretation as your "1 entity" view).

Neither that per-district system, nor my original popular vote proportional system, would require a parliamentary style of government. Indeed, under a parliamentary system, the executive would be chosen by parliament itself and there would be no need for the electoral college or even the presidential vote at all.

The constitution literally says the States shall choose the president.

Not the people.

States are people, my friend.

(Hopefully that's a less controversial statement than Romney's famous line).